How will rivers of living water flow from believers (John 7:38)?

In John 7:38, Jesus makes a seemingly odd metaphorical statement: “Whoever believes in me, as Scripture has said, rivers of living water will flow from within them.” Yet, as it turns out, the statement isn’t so odd, because Jesus actually had much to say about the idea of water and new life.
In John 4:10 Jesus tells the Samaritan woman that He could give her “living water.” This was in contrast to the physical water that the Samaritan woman came to the well to retrieve. That physical water would run out, and she would need to continually return to get more. But Jesus offered the woman water that would never run out—water that would become within the believer “a spring of water welling up to eternal life” (John 4:14). Jesus later would return to this theme when He stood up in public and said, “If anyone is thirsty let him come to Me and drink” (John 7:37). In this way, He was again offering Himself as the water of life and telling all they could come to Him and receive that never-ending life.
After making the offer of life-giving water, Jesus adds that rivers of living water would flow from the heart of the believer (John 7:38). Jesus alludes to Isaiah 55:1 and Isaiah 58:11—passages that similarly present the Messianic hope in terms of life-giving water (cf. Exodus 17:1–6; Psalm 78:15–16; 105:40–41; Proverbs 18:4; Isaiah 12:3; Ezekiel 47:1–11; and Zechariah 14:8). Jesus was not simply using metaphor to liken His own life-giving ministry to that of water. He was actually claiming to be the fulfillment of Scripture’s water allusions and prophecies. Because He was the Life-giver, those who believed in Him would have eternal life within them and would no longer need to seek for life from external sources. Later, it is revealed that God would put His Spirit within each believer (Romans 8:9), and each believer would have eternal life (John 6:47) and the evidence of life (in the Holy Spirit) within. It is in that sense that “rivers of living water” would flow from the hearts of believers.
Later, Paul would describe that in love Christ sanctifies His church, washing her with the water of His word (Ephesians 5:25–26). The writer of Hebrews continues the theme, noting that our hearts are sprinkled and “our bodies washed with pure water” (Hebrews 10:22). Peter adds that believers are cleansed as if by water (1 Peter 3:20–21). Finally, in a beautiful portrayal of Jesus’ ministry, John says that the Lamb would be the Shepherd, leading His people to the water of life (Revelation 7:17). This is reminiscent of David’s song of Psalm 23 in which the Shepherd leads David beside quiet waters (Psalm 23:2) and restores his soul. Just as each of these writers recognized, we need to understand that Jesus is the One who freely gives eternal life.